Exam 16: Analysis of Categorical Data

A suburban realtor is studying commuter time in the Houston metropolitan area.She has been told the average weekday travel time from a southern suburb at 8:00am is 45 minutes.For five months she counts the number of days that it takes her more than 45 minutes to arrive in downtown when she leaves her house at 8:00am.She expects the data are uniformly distributed across the five months.Her sample of observed data yields the following frequencies 9 days,15 days,8 days,11 days,12 days.Using $\alpha$ = .10,the appropriate decision is _______.

A market researcher is studying the use of coupons by consumers of varying ages.She classifies consumers into four age categories and counts the number of grocery store customers who use at least one coupon during check out.It is expected that data are uniformly distributed across the four age categories.The observed data results in frequencies of 22,35,32,and 21.Using $\alpha$ = .05,the observed chi-square value is _______.

The number of degrees of freedom in a chi-square goodness-of-fit test is the number of categories minus the number of parameters estimated.

A chi-square goodness-of-fit test to determine if the observed frequencies in seven categories are uniformly distributed has six degrees of freedom.

The null hypothesis for a chi-square test of independence is that the two variables are not related.

Anita Cruz recently assumed responsibility for a large investment portfolio.She wonders whether industry sector influences investment objective.Her staff prepared the following contingency table from a random sample of 200 common stocks. Using $\alpha$ = .01,critical chi-square value is ______________.

When using the chi-square goodness-of-fit test,the type of distribution (uniform,Poisson,normal)being used does not influence the hypothesis test.

A contingency table is to be used to test for independence.There are 3 rows and 3 columns in the table.How many degrees of freedom are there for this problem?

A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased.The following is a contingency table from a random sample of 300 individuals. Using $\alpha$ = .05,observed chi-square value is ______________.

Anita Cruz recently assumed responsibility for a large investment portfolio.She wonders whether industry sector influences investment objective.Her staff prepared the following contingency table from a random sample of 200 common stocks. Using $\alpha$ = .01,observed chi-square value is ______________.

Use the following set of observed frequencies to test the independence of the two variables.Variable one has values of 'A' and 'B'; variable two has values of 'C','D',and 'E'. Using $\alpha$ = 0.05,the observed chi-square value is _______.

A market researcher is studying the use of coupons by consumers of varying ages.She classifies consumers into four age categories and counts the number of grocery store customers who use at least one coupon during check out.It is expected that data are uniformly distributed across the four age categories.The observed data results in frequencies of 22,35,32,and 21.Using $\alpha$ = .05,the critical chi?square value is _______.

A chi-square goodness of fit test is to be performed to see if data fit the Poisson distribution.There are 8 categories,and lambda must be estimated.How many degrees of freedom should be used?

A suburban realtor is studying commuter time in the Houston metropolitan area.She has been told the average weekday travel time from a southern suburb at 8:00am is 45 minutes.For five months she counts the number of days that it takes her more than 45 minutes to arrive in downtown when she leaves her house at 8:00am.She expects the data are uniformly distributed across the five months.Her sample of observed data yields the following frequencies 9 days,15 days,8 days,11 days,12 days.Using $\alpha$ = .01,the critical chi-square value is _______.

A gasoline distributor wonders whether an individual's income level influences the grade of gasoline purchased.The following is a contingency table from a random sample of 300 individuals. The estimate of the expected number of individuals with income less than $30,000 who purchase regular gasoline when income and type of gasoline are independent is _______.

A cancer research group surveys 100 women more than 40 years old to test the hypothesis that 50% of women in this age group have regularly scheduled mammograms.Forty of the women respond affirmatively.Using $\alpha$ = 0.05,the critical value of chi-square is _______.

Sam Hill,Director of Media Research,is analyzing subscribers to the TravelWorld magazine.He wonders whether subscriptions are influenced by the head of household's highest degree earned..His staff prepared the following contingency table from a random sample of 300 households. Using $\alpha$ = .05,the critical value of chi-square is ______________.

Catherine Chao,Director of Marketing Research,is evaluating consumer acceptance of alternative toothpaste packages.She wonders whether acceptance is influenced by children in the household.Her staff prepared the following contingency table from a random sample of 100 households. Using $\alpha$ = .05,the appropriate decision is ______________.

Sam Hill,Director of Media Research,is analyzing subscribers to the TravelWorld magazine.He wonders whether subscriptions are influenced by the head of household's highest degree earned.His staff prepared the following contingency table from a random sample of 300 households. Using $\alpha$ = .05,the appropriate decision is ______________.

Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution.He collected a random sample and constructed the following frequency distribution to test his hypothesis. Using $\alpha$ = 0.05,the critical value of chi-square for this goodness-of-fit test is ____.